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Topological quantum field theory and invariants of graphs for quantum groups


Beliakova, A; Durhuus, B (1995). Topological quantum field theory and invariants of graphs for quantum groups. Communications in Mathematical Physics, 167(2):395-429.

Abstract

On the basis of generalized 6j-symbols we give a formulation of topological quantum field theories for 3-manifolds including observables in the form of coloured graphs. It is shown that the 6j-symbols associated with deformations of the classical groups at primitive even roots of unity provide examples of this construction. Calculational methods are developed which, in particular, yield the dimensions of the state spaces as well as a rather simple proof of the relation, previously found by Turaev and Walker for the case ofU q (sl(2,C)), between these models and corresponding ones based on the ribbon graph construction of Reshetikhin and Turaev.

Abstract

On the basis of generalized 6j-symbols we give a formulation of topological quantum field theories for 3-manifolds including observables in the form of coloured graphs. It is shown that the 6j-symbols associated with deformations of the classical groups at primitive even roots of unity provide examples of this construction. Calculational methods are developed which, in particular, yield the dimensions of the state spaces as well as a rather simple proof of the relation, previously found by Turaev and Walker for the case ofU q (sl(2,C)), between these models and corresponding ones based on the ribbon graph construction of Reshetikhin and Turaev.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistical and Nonlinear Physics
Physical Sciences > Mathematical Physics
Language:English
Date:1995
Deposited On:19 Apr 2010 10:51
Last Modified:26 Jun 2022 22:43
Publisher:Springer
ISSN:0010-3616
Additional Information:The original publication is available at www.springerlink.com
OA Status:Green
Publisher DOI:https://doi.org/10.1007/BF02100592
  • Content: Accepted Version